Holographic storage using shift multiplexing

ABSTRACT

The invention is embodied in a method of recording successive holograms in a recording medium, using at least a fan of M waves along at least a first axis with a separation angle between adjacent waves and directing the fan of M waves as a reference beam along a reference beam path onto the recording medium, successively modulating a wave with a succession of images to produce a succession of signal beams along a signal beam path lying at a propagation angle relative to the reference beam path so that the signal and reference beams intersect at a beam intersection lying within the medium, the beam intersection having a size corresponding to beam areas of the reference and signal beams, producing a succession of relative displacements in a direction parallel to the first axis between the recording medium and the beam intersection of the signal and reference beam paths in synchronism with the succession of signal beams, each of the displacements being less than the size of the intersection whereby to record successive holograms partially overlapped along a direction of the displacements.

BACKGROUND OF THE INVENTION Origin of the Invention

The U.S. Government has certain rights in this invention pursuant toGrant No. F49620-92-J-0400 awarded by the United States Air Force.

TECHNICAL FIELD

The present invention relates to holographic memories, holographicstorage systems and holographic processors.

BACKGROUND ART

The traditional advantages of 3-D holographic memories are high storagedensity and parallel access capability. These features were recognizedin the early 1960's and serious efforts towards the practicalimplementation of such memories were undertaken. Unfortunately, theseefforts did not produce commercially viable memories. In recent yearsthere has been a resurgence of interest in 3-D optical storage due to aconsiderable improvement in the understanding and availability ofstorage media, a dramatic improvement in optoelectronic components ingeneral, and most importantly, the emergence of applications, such asimage processing, neural networks, and data bases where the capabilitiesof these memories can be effectively utilized. This recent activity hasculminated in the storage of 10⁴, 320×220-pixel holograms in a volumeroughly equal to 2 cm³. If spatial light modulators with 1 millionpixels are used, then the storage density achievable today is in excessof 10⁹ bits per cm³.

Volume holograms are usually recorded using angular, wavelength, phasecode, and spatial multiplexing. In addition, peristrophic multiplexing,a holographic technique that applies to either thin or thick (3-D)media, was recently introduced. Any of these methods, or certaincombinations of them, can be used to multiplex holograms for holographicstorage devices. All of these methods employ a reference beam consistingof a single plane wave, which may have a phase code imprinted on thewavefront.

It is an object of the present invention to exploit the use of non-planewaves in the reference beam to implement multiplexing. It is a furtherobject of the invention to perform multiplexing without requiringanything more than a relative translation between the holographicrecording media and optical (signal and reference) beams.

SUMMARY OF THE INVENTION

The invention is embodied in a method of recording successive hologramsin a recording medium, using at least a linear fan of M waves along afirst axis with a separation angle between adjacent waves and directingthe fan of M waves as a reference beam along a reference beam path ontothe recording medium, successively modulating a wave with a successionof images to produce a succession of signal beams along a signal beampath lying at a propagation angle relative to the reference beam path sothat the signal and reference beams intersect at a beam intersectionlying within the medium, the beam intersection having a sizecorresponding to beam areas of the reference and signal beams, producinga succession of relative displacements in a direction parallel to thefirst axis between the recording medium and the beam intersection of thesignal and reference beam paths in synchronism with the succession ofsignal beams, each of the displacements being less than the size of theintersection whereby to record successive holograms partially overlappedalong a direction of the displacements. Preferably, the first axis andthe signal beam path are parallel and the separation angle of the fan ofM waves is at least approximately equal to the beam wavelength dividedby the product of the medium thickness and the tangent of thepropagation angle. Preferably, each of the relative displacements is ofa length at least approximately equal to the wavelength divided by theproduct of M is multiplied by the separation angle. The methodpreferably includes temporarily halting the succession of signal beamsafter a predetermined number of the relative displacements have beenproduced and moving the recording medium and the beam intersectionrelative to one another until the beam intersection does not intersectthe first one of the holograms recorded with the succession of relativedisplacements, and then resuming the producing of a succession of signalbeams and the producing of a succession of relative displacements.Preferably, the predetermined number of relative displacements is equalto M.

The fan of M waves include waves within the class of radiation wavesincluding plane waves, cylindrical waves and elliptical waves. Therecording medium may be disk-shaped and the successive relativedisplacements are achieved by rotating the recording medium. In analternative embodiments M is equal to infinity whereby the fan of Mwaves is a single spherical wave.

In a two-dimensional shift multiplexing embodiment, the reference beamis a two-dimensional fan of waves, the linear fan of M waves beingincluded within the two-dimensional fan of waves, the two dimensionalarray including M waves along the first axis and N waves along a secondaxis, the M waves of the first axis being separated by the separationangle and the N waves of the second axis being separated by an otherseparation angle, the method further including producing an otherrelative displacement between the recording media and the beamintersection in a direction parallel to the second axis, the otherrelative displacement being less than the size of the beam intersection.Preferably, the second axis and the signal beam path are approximatelynormal to one another and the other separation angle is approximatelyequal to the square root of the quotient of the wavelength of thereference beam divided by the thickness of the recording medium.Moreover, the other relative displacement is approximately thewavelength of the reference beam divided by the product of N multipliedby the other separation angle. The recording medium may be disk-shaped,the tracks may be circular and the second axis lies in a radialdirection relative to the disk-shaped recording medium, wherebysuccessive tracks partially overlap along the radial direction.

The holograms include one of (a) image plane holograms, (b) Fouriertransform holograms, (c) Fresnel plane holograms.

The fan of M waves may be provided by diffracting a single beam into aline of plural wave sources separated by a spacing, and focusing theplural wave sources through a lens having a focal length, the focallength and the spacing being a function of the separation angle. In thiscase, the lens may be one of (a) spherical, (b) elliptical, (c)cylindrical so that the fan of M waves are one of (a) plane waves, (b)elliptical waves, (c) cylindrical waves, respectively. Alternatively,the reference beam is a spherical wave provided by focusing a coherentplane wave beam through a spherical lens, so that M is infinity.

In accordance with another aspect, the invention is embodied in a methodof reconstructing at a detection plane successive holograms previouslyrecorded in a recording medium by diffracting a succession of signalbeams with a reference beam including a linear fan of M waves, thelinear fan being parallel to the path of the signal beams and having aseparation angle between adjacent waves of the fan, while successivelydisplacing the medium relative to the signal and reference beams in adirection parallel to the first axis by a distance less than theintersection of the reference and signal beams in the recording mediumin synchronism with the succession of signal beams, the method ofreconstructing including: providing at least a linear fan of M wavesalong a first axis corresponding to the direction of the reference beamwith which the holograms were previously recorded with a separationangle between adjacent waves and directing the fan of M waves as areference beam along a reference beam path onto the recording medium,producing a succession of relative displacements in a direction parallelto the first axis between the recording medium and the beam intersectionof the signal and reference beam paths in synchronism with thesuccession of signal beams, each of the displacements being equal to thedistance of the displacements with which the holograms were previouslyrecorded, and detecting at the reconstruction plane light diffractedfrom the reference beam by a succession of the previously recordedholograms.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic block diagram of a holographic storage system inaccordance with one embodiment of the invention employing multiple planewaves in the reference beam.

FIG. 2 is a diagram illustrating an embodiment of the inventionemploying disk-shaped recording media for multiplexing in thealong-track direction.

FIG. 3 is a diagram illustrating the placement of successive hologramson a disk media.

FIG. 4 is a diagram correspoding to FIG. 3 illustrating how tracks areoverlapped by multiplexing in the radial direction.

FIG. 5 is a diagram of an output face of a point source array employedin the embodiment of FIG. 4.

FIG. 6 is a schematic block diagram corresponding to FIG. 1 of anotherembodiment employing a single spherical wave in the reference beam.

FIG. 7A is a schematic block diagram illustrating a variation of theembodiment of FIG. 1 in which the signal and reference beams illuminateopposite sides of the recording film.

FIG. 7B is a schematic block diagram illustrating a variation of theembodiment of FIG. 6 in which the signal and reference beams illuminateopposite sides of the recording film.

FIG. 8 is a simplified block diagram illustrating a variation of theembodiment of FIG. 1 or 6 in which the signal and reference beams areorthogonal.

FIG. 9 is a graph illustrating the effect of shift along the x-directionon a hologram sensed at the reconstruction plane in the embodiment ofFIG. 1.

FIG. 10 is a graph illustrating the light intensity as a function ofposition in the x-direction as sensed at the reconstruction plane in theembodiment of FIG. 1 corresponding to three multiplexed holograms whosepeaks are labelled, respectively, A, B, C in the graph.

FIG. 11 is a graph illustrating the shift selectivity achieved in theembodiment of FIG. 6 for three different media-to-spherical wave sourcedisplacements and three different values of the numerical aperture ofthe spherical wave.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention multiplexes holograms using a reference beamconsisting of a spectrum of plane waves (similar to phase codemultiplexing, for example). Multiplexing is achieved by shifting(translating) the recording medium with respect to the signal andreference beams. Alternatively the two beams can be translated in tandemwith respect to the stationary medium.

FIG. 1 illustrates a holographic memory system in accordance with afirst embodiment of the invention. A laser 10 furnishes a laser beam 12to a diffractive element 14 which produces from the laser beam 12 anarray of M plane waves. The M plane waves are then Fourier transformedby a spherical lens 15 into M beam sources 16 separated by uniformdistances d. The light from the array of M beam sources 16 istransformed into a one-dimensional fan of M plane waves 18 by aspherical lens 20. The fan of plane waves 18 constitutes the referencebeam for holographic recording and reproduction. The diffractive element14 could be a Dammann grating of the type disclosed in Dammann et al.,"High Efficiency In-Line Multiple Imaging by Means of Multiple PhaseHolograms," Optics Communications, Vol. 3, No. 5 pages 312-315 (July1971). However, in one implementation, the diffractive element 14 was ahologram with similar properties. The spherical lenses 15 and 20 havefocal lengths F_(r) and image the reference beam emanating from thediffractive element 14 onto a recording spot in an optical recordingmedium 22. As indicated in FIG. 1, the distances between (a) thediffractive element 14 and the center of the spherical lens 15, (b) thecenter of the spherical lens 15 and the plane of beam sources 16, (c)the plane of beam sources 16 and the center of the spherical lens 20,and (d) the center of the spherical lens 20 and the plane of therecording medium 22 are each preferably F_(r).

A beam splitter 24 splits the laser beam 12 between the diffractiveelement 14 and a mirror 26. That portion of the laser beam 12 divertedto the mirror 26 is modulated by a spatial light modulator 28 to providea signal beam 29 for recording a hologram in the optical recordingmedium 22.

During recording of a hologram in the medium 22, recording electronics27 controls the spatial light modulator 28 in accordance with aninformation signal representing either an image or an array of data. Thesignal beam 29 is imaged by spherical lenses 30 and 31, each of focallength F, onto the same recording spot in the medium 22 that isilluminated by the reference beam 18. The distances between (a) thespatial light modulator 28 and the center of the spherical lens 30, (b)the center of the spherical lens 30 and a half-way point P with thecenter of the next spherical lens 31, and (c) the center of thespherical lens 31 and the recording spot in the medium 22 are eachpreferably a uniform displacement F.

For reconstruction of a hologram previously recorded in the recordingmedium 22, the reference beam 18 is applied as illustrated in FIG. 1while the signal beam 29 is blocked. The diffracted beam 35 emanatingfrom the recording medium 22 is imaged through spherical lenses 32 and33, each of focal length F, onto the plane of a detector 34. Thedistances between (a) the recording spot in the medium 22 and the centerof the lens 32, (b) the center of the lens 32 and a midpoint P' with thecenter of the next lens 33, (c) the midpoint P' and the center of thelens 33 and (d) the center of the next lens 33 and the plane of thedetector 34 are each preferably the uniform displacement F. The detector34 may be an array of image pixels such as a charge coupled device imagedetector. A servo 36 under control of the recording electronics 27governs the amount of shift between the medium and the optical beams 18,29 with the recording of successive holograms.

The description of the preceding two paragraphs with reference to FIG. 1is pertinent to image plane holography using a 4-F imaging system.Alternatively, imaging can be performed using a single lens of focallength F located a distance d_(i) from the SLM 28 and a distance d₀ fromthe recording medium 22, the distances d_(i) and d₀ satisfying the lenslaw with respect to the lens focal length F: d₀ ⁻¹ +d_(i) ⁻¹ =F⁻¹. Thesame method of using a single lens can be used for imaging thereconstruction of holograms onto the CCD sensor 34.

Alternative holographic methods include Fourier holography and Fresnelholography. To implement Fourier plane holography, we remove the lenses30 and 32 and align the SLM 28 on the mid-point denoted by P in FIG. 1(which is a distance F from the lens 31) for recording; and we align theCCD sensor 34 on the plane P' (which is a distance F from the lens 33)for reconstruction. In that case, the Fourier transform of the signalbeam (as modulated by the SLM 28) appears through the lens 31 on theplane perpendicular to the signal beam axis PP' intersecting the centerof the recording material 22, and is recorded as a hologram. On theother hand, the reconstruction undergoes a second Fourier transform (bythe lens 32) forming the original image (inverted) on the CCD sensor 34.To implement Fresnel plane holography, we alter the Fourier planegeometry as follows: In FIG. 1, the lenses 30 and 32 are not present,the SLM is located at plane P and the CCD sensor 34 is located at planeP', the recording medium 22 is located a distance d₁ from the lens 31and a distance d₂ from the lens 33 such that d₁ +d₂ =2F. (The specialcase of d₁ =d₂ =F reduces to Fourier plane holography.) The operation inthe Fresnel holography case is similar to that of the Fourier holographycase, except that a defocused version of the Fourier transform isrecorded as a hologram. In the remaining portion of the description ofFIG. 1, it will be assumed that Fourier transform holograms are beingrecorded or reconstructed, so that the lenses 30 and 32 depicted in FIG.1 are not present, the SLM 28 is located on the plane P, and the CCDsensor 34 is located on the plane P'.

The reference beam 18 originates from the array 16 of M point sourceslocated in the front focal plane of the Fourier lens 20, and centeredaround the optical axis z. The lens 20 transforms the field into the fan18 of M plane waves. The angular separation is uniform, given byΔθ≈d/F_(r) where d is the distance between successive point sources andF_(r) is the focal length. Thus the angle of incidence of the m-thcomponent is: ##EQU1##

The signal beam 29 will have more than one angular component because ofthe modulation imposed by the spatial light modulator 28. The angle ofincidence of the central component of the signal beam with respect tothe z-axis is denoted by θ_(S). Because the reference consists of Mplane waves, the recorded image may be thought of as consisting of Mseparate holograms recorded simultaneously with the same signal beam.During reconstruction, each plane wave in the reference fan 18 reads outnot only the hologram it recorded, but also all the holograms recordedby the other plane waves of the reference fan. These additionalreconstructions, or "ghosts", produce images that are shifted withrespect to the primary reconstruction, due to the change in read-outangle relative to the recording angle. The ghosts are Bragg mismatchedby an amount roughly proportional to the angular separation between theplane wave component that originally recorded the hologram and thecomponent that is reconstructing it. For the hologram recorded betweenthe central signal component and the m=0-th reference component theamount of Bragg mismatch is Δk_(z) =2π1tan θ_(S) Δθ/λ when read out bythe ±1-th reference component. The same relation holds approximately forthe other holograms. The diffraction efficiency of these Braggmismatched holograms is proportional to ##EQU2## where sinc(χ)=sinπχ/(πχ) and L is the thickness of the recording medium.

It follows that by choosing the angular separation Δθ between thereference components such that the sinc function of eq. 2 vanishes, theghosts will be eliminated, leaving a clean reconstruction. From eq. 2the required separation is: ##EQU3##

This equation constrains the design of the diffractive element 14 inthat, for a given focal length F_(r) of the lens 20, the separation dbetween adjacent point sources 16 must be ##EQU4## in the paraxialapproximation.

Having eliminated the ghosts, this specification now examines whathappens to the diffracted light if the hologram is shifted by a distanceγ in the χ-direction. The diffracted field ε_(d) is obtained bymultiplying the illuminating reference (consisting of M plane waves) bythe expression for the M recorded holograms shifted by γ. For a hologramrecorded with a single plane wave signal beam of incidence angle θ_(S),the diffracted field at the reconstruction plane is: ##EQU5##

The three dimensional nature of the hologram (i.e. the z dependence andthe constraint imposed on the angular separation between plane waveswithin the fan 18 by Equation 4) serves to eliminate the cross-termsm≠m' (ghosts) from the double summation. From eq. 6, the diffractedfield consists of the reconstruction of the signal at angle θ_(S)weighted by a sum leading to the familiar array function. Therefore theintensity of the diffracted field as a function of shift is: ##EQU6##

The zeros of the array function occur at ##EQU7##

Multiplexing is performed by recording each successive hologram(corresponding to a successive image on the light modulator 28) with aspatial shift γ=λ/MΔθ with respect to its two neighbor holograms.Because of the periodicity of the array function, at maximum M hologramscan be superimposed on the same location for multiplexing along the χdirection in the drawing of FIG. 1. The period is: ##EQU8##

The shift multiplexing method is particularly well-suited for theimplementation of holographic 3-D disks. A 3-D disk can be readilyimplemented with this method by simply using the disk rotation (which isalready part of the system intended to allow accessing of information ondifferent locations on the disk surface) in order to implement theshift. This simplifies the design of the head since no additionalcomponents are required for selective readout.

FIG. 2 illustrates how the embodiment of FIG. 1 is implemented inaccordance with the foregoing using a disk medium rotated by the servo36 of FIG. 1 under control of the recording electronics 27 of FIG. 1. Inthe embodiment of FIG. 2, it may be possible to eliminate the lenses 15,20, depending upon the selected characteristics of the diffractiveelement 14. FIG. 3 illustrates the placement of successive hologramswithin the recording medium 22. Referring to FIG. 3, the medium 22 is anoptical disk divided into plural longitudinal circular tracks 40labelled N, N+1, and so forth. In the embodiment of FIG. 3, adjacenttracks do not overlap but may be arbitrarily close together. As shown intrack N, a series of M (in this case M=5) holograms are recorded, thedisk being rotated between subsequent recordings by an angle ##EQU9##where R_(N) is the radius of track N. This corresponds to a spatialshift of ##EQU10## with the recording of each hologram. Then, after Mholograms have been recorded within the period length ##EQU11##recording is temporarily halted while the disk is rotated until the beamspot (the intersection of the reference and signal beams in the medium22) is beyond the boundary of the first-recorded hologram in the seriesof M holograms previously recorded in the period length γ_(M). Then, theentire process is repeated, with M new holograms being recorded(indicated in dashed line in FIG. 3). The "skip" length by which thedisk is rotated while recording is temporarily halted is the lengthL_(h) of one hologram (as measured in the plane of the surface of thedisk) minus M×the shift displacement between successive holograms γ, orL_(h) -M.sub.γ. In this way, no spot along the entire length of thetrack has more than M holograms multiplexed along the x-direction.

Preferably, the foregoing recording process is implemented by the shiftservo 36 under the control of the recording electronics 27.Specifically, the recording electronics 27, which may comprise, forexample, a programmed microprocessor, causes the servo 36 to rotate thedisk media 22 to a first position, at which time the recordingelectronics 27 causes the spatial light modulator to transmit a firstimage on the laser beam 29. The image is then recorded on the media 22.Thereafter, the servo 36 rotates the disk media 22 by the shiftdisplacement γ. Thereafter, the recording electronics causes the spatiallight modulator to transmit the next image on the laser beam 29. Theforegoing process is repeated until M holograms have been recorded inthis manner, at which time the recording electronics 27 causes the servo36 to rotate the disk by the skip length L_(h) -M.sub.γ before recordingthe next series of holograms. Once an entire track (for example track N)has been filled, the recording electronics 27 causes servoes 45controlling optical elements in the paths of the reference and signalbeams (such as the reference lens 20 and the signal lens 30) to move soas to radially move the beam spot at which the signal and referencebeams intersect inside the disk media 20 by the width of one track(i.e., by the width of one beam spot).

The size of each hologram along one side (as measured in a planeperpendicular to the signal beam) may be expressed as the number ofpixels N_(P) along each side of the hologram multiplied by the pixelsize δ, or N_(P) δ. However, as measured in a plane parallel to thesurface of the disk media 22, the size of one hologram is Ltanθ_(S)+N_(P) δ/cosθ_(S). The first term Ltan θ_(S) is attributable to theangle θ_(S) between the reference beam and the z-axis. The factorcosθ_(S) is attributable to fact that the signal beam is slanted withrespect to the plane of the disk media 22.

Preferably, the projection of the signal beam 29 onto the disk is astraight line which is parallel to the χ-direction or direction ofmotion of the disk near the hologram being recorded. This optimizesselectivity along the χ-direction.

While the embodiment of FIG. 3 has no overlapping of adjacent tracks(i.e., multiplexing of holograms along the radial or y-direction),overlapping of adjacent tracks may be achieved as illustrated in FIG. 4by selecting a diffractive element 14 which provides a two-dimensionalarray of beam sources 16 rather than the line of beam sources disclosedhereinabove. The limitation on the spacing γ_(y) between adjacentholograms along the radial or y-direction is governed by the sameprinciples as those discussed above with respect to the spacing γ alongthe x- direction, with the exception that required angular separation ofthe fan of reference beams along the radial or y-direction is: ##EQU12##The output face of the Dammann grating or diffractive element 14 asFourier transformed by the lens 15 is illustrated in FIG. 5, in whichthe spacing between point sources in the along-track or x-direction is##EQU13## as stated above, while the spacing in the radial ory-direction is ##EQU14## In the two-dimensional array diffractiveelement 14 of FIG. 5, the number of point sources M in the along-trackor x-direction may be greater than the number of point sources M_(y) inthe radial or y-direction. Thus, the incremental shift spacing γ betweensuccessive holograms along the x-direction is as given above, namelyγ=λ/MΔθ, while along the y-direction the incremental shift spacing γ_(y)between successive holograms is γ_(y) =λ/M_(y) Δθ_(y), where Δθ_(y)≈d_(y) /F_(r).

The storage density D per unit area that the invention can achieve inthe embodiment of FIG. 1 is determined by the thickness-dependentangular selectivity (eq. 10), the number of beams M allowed by theoptics, the page size N_(P) δ (δ is the pixel size and N_(P) the numberof pixels) and the periodicity of the array function. An approximateformula for the density is: ##EQU15## when shift-multiplexing in onedimensional only.

For L=100 μm and signal incidence angle θ_(S) =30°, usage of F/1 opticsallows M=100 holograms. Then, for typical page parameters N_(P) =1000,δ=2 μm, eq. 12 yields D=21.1 bits/μm².

In the embodiment of FIG. 6, shift multiplexing is implemented using aspherical wave reference instead of the fan of M plane waves. TheDammann grating or diffractive element 14 is removed so that thespherical lens 20 provides a single spherical wave as the reference beam18. The spherical wave reference beam of this embodiment is a specialcase of the multiple plane wave embodiment of FIG. 1 in which there areat least nearly an infinite number of plane waves distributed in atwo-dimensional plane and separated by infinitely small separationangles. The analysis of the embodiment of FIG. 6 is as follows: Considera spherical reference wave originating a distance z₀ from the center ofthe recording material and a plane wave signal incident at angle θ_(S)with respect to the optical axis. The displacement z₀ is preferablyselected so that the reference beam spot size matches the signal beamspot size at their intersection within the media 22. An approximatecalculation (under the paraxial and Born approximations and neglectingvariable modulation depth) predicts that the shift selectivity isrelated to the focal distance and the Bragg angular selectivity (eq. 10)as γ_(Bragg) ≈z₀ Δθ=λz₀ /Ltan θ_(S). The finite numerical aperture (NA)broadens the selectivity curve by a factor of γ_(NA) ≈λ/2(NA). Thereforewe have: ##EQU16##

One advantage of the single spherical wave embodiment of FIG. 6 is thatthe spherical wave reference beam corresponds to a two-dimensional fanof an infinite number of plane waves each of infinitesimal power with aninfinitesimally small separation angle between waves, so that there isno periodicity (i.e., γ_(M) is infinite) and two-dimensionalmultiplexing (as in FIG. 5) may be performed if desired because of thetwo-dimensional nature of the spherical wave reference beam.

FIG. 7A illustrates an arrangement in which the signal and referencebeams in the embodiment of FIG. 1 illuminates opposite sides of therecording medium 22 and are at least nearly coaxial. The beam splitter24 separates the reference beam from the reconstructed beam duringhologram reconstruction. The lenses 20 and 37 image the diffractiveelement 14 onto the disk media 22, thus providing the reference beam.The lenses 30 and 36 image the spatial light modulator 28 onto the diskmedia 22, thus providing the signal beam. During hologramreconstruction, light to the spatial light modulator 28 is blocked whilethe lenses 20, 32 image the reconstruction onto the detector 34. Theembodiment of FIG. 7A is useful for thin optical media such as polymerfilms on the disk 22.

FIG. 7B illustrates a variation of the geometry of the embodiment ofFIG. 7A for using a spherical wave, in which the reference beam isperpendicular to the plane of the disk media 22 while the signal beamand reconstructed beams make an acute angle with the plane of the diskmedia 22. The embodiment of FIG. 7B is suitable for thick recordingmedia such as a Lithium Niobate crystal.

FIG. 8 illustrates an arrangement in which the signal and referencebeams of either the embodiments of FIGS. 1 or 6 are mutuallyperpendicular. The embodiment of FIG. 8 is useful for thick opticalmedia such as a LiNO3 crystal. This embodiment achieves thetheoretically smallest required shift distance. Experimentally, we havedemonstrated shift selectivity of 2 μm in the X direction and 10 μm inthe Y direction using an 8 mm thick Lithium Niobate crystal inimplementing the embodiment of FIG. 8. The embodiment of FIG. 8 may bemodified so that the reference beam is a single spherical wave (as inthe embodiment of FIG. 6) by eliminating the diffusion element 14 andthe lenses 15 and 20.

A working example of the embodiment of FIGS. 1-3 was demonstrated usinga reference fan of 20 plane waves angularly separated by 0.5°. Thediffractive element 14 was a hologram rather than a Dammann grating. Therecording material was DuPont HRF-150 polymer of thickness L=38 μm. Theeffect of shift on the reconstruction of a single hologram is shown inFIG. 9. The signal image was a 100×100 random bit pattern. For theparticular parameters the theoretical shift selectivity is 2.8 μm andthe period is 55 μm, in good agreement with the experiment. The reasonthe periodic reconstructios are weaker is the finite transverse size ofthe hologram of the diffractive element 14.

FIG. 9 is useful for illustrating the recording method of the invention.The peak width γ is inversely proportional to the number M of the planewaves in the fan. The spacing between peaks γ_(M) limits to M the numberof other holograms (indicated in dashed line in FIG. 9) that can bestored between peaks of the first hologram.

The response at the reconstruction plane of the detector 34 for threeholograms obtained with the embodiment of FIGS. 1-3 are shown in FIG.10. Each hologram is reconstructed periodically, following its own arrayfactor. Because of the very small thickness of the recording medium inthis experiment, we used angular separation smaller than that predictedby eq. 10. Therefore the ghosts had to be filtered out in the Fourierplane in this example.

For the embodiment of FIG. 6, the graph of FIG. 11 shows theexperimental shift selectivity curves for z₀ =9, 14, 24 mm and NA of0.3, 0.15, and 0.075, respectively. The angle of incidence of the signalbeam was 40° outside the 8 mm thick iron doped LiNbO₃ crystal(refractive index n≈2.24). The experimental selectivity agrees with eq.13.

While the invention has been described with reference to embodiments inwhich the reference lens 20 is spherical (so as to provide either a fanof plane waves as in FIG. 1 or a single spherical wave as in FIG. 6),the shift multiplexing of the invention described above may also beachieved using different types of reference beams other than a singleplane wave. For example, cylindrical waves may be employed (in whichcase the reference lens 20 is a cylindrical lens) or elliptical wavesmay be employed (in which case the reference lens 20 is an ellipticallens). In general, the invention may employ any one of a large varietyof non-planar reference waves to attain shift-selective properties inholographic reconstruction. Multiple plane waves and a spherical waveare but two examples of non-planar wavefronts, but the invention is notlimited thereto. Clearly, any generalization of non-planar wavefrontsmay be employed in carrying out the invention.

While the invention has been described in detail by specific referenceto preferred embodiments, it is understood that variations andmodifications thereof may be made without departing from the true spiritand scope of the invention.

What is claimed is:
 1. A method of recording successive holograms in arecording medium, comprising:providing at least a fan of M amount ofwaves along at least a first axis with a separation angle betweenadjacent waves and directing said fan of M waves as a reference beamalong a reference beam path onto said recording medium; successivelymodulating a wave with a succession of images to produce a succession ofsignal beams along a signal beam path lying at a propagation anglerelative to said reference beam path so that said signal and referencebeams intersect at a beam intersection lying within said medium, saidbeam intersection having a size corresponding to beam areas of saidreference and signal beams; producing a succession of relativedisplacements a direction parallel to said first axis between saidrecording medium and said beam intersection of said signal and referencebeam paths in synchronism with said succession of signal beams, each ofsaid displacements being less than said size of said intersectionwhereby to record successive holograms partially overlapped along adirection of said displacements; and wherein said first axis and saidsignal beam path are parallel and said signal beam and said M amount ofwaves of said reference beam have a wavelength, said recording mediumhas a thickness and said separation angle of said fan of M waves is atleast approximately equal to ##EQU17## wherein λ is the wavelength, L isthe thickness, and θ_(S) is the propagation angle.
 2. A method ofrecording successive holograms in a recording medium,comprising:providing at least a fan of M amount of waves along at leasta first axis with a separation angle between adjacent waves anddirecting said fan of M waves as a reference beam along a reference beampath onto said recording medium; successively modulating a wave with asuccession of images to produce a succession of signal beams along asignal beam path lying at a propagation angle relative to said referencebeam path so that said signal and reference beams intersect at a beamintersection lying within said medium, said beam intersection having asize corresponding to beam areas of said reference and signal beams;producing a succession of relative displacements a direction parallel tosaid first axis between said recording medium and said beam intersectionof said signal and reference beam paths in synchronism with saidsuccession of signal beams, each of said displacements being less thansaid size of said intersection whereby to record successive hologramspartially overlapped along a direction of said displacements; andwherein said signal beam and said M amount of waves of said referencebeam have a wavelength and each of said relative displacements is of alength at least approximately equal to ##EQU18## wherein λ is thewavelength and θ is the separation angle.
 3. A method of recordingsuccessive holograms in a recording medium, comprising:providing atleast a fan of M amount of waves along at least a first axis with aseparation angle between adjacent waves and directing said fan of Mwaves as a reference beam along reference beam path onto said recordingmedium; successively modulating a wave with a succession of images toproduce a succession of signal beams along a signal beam path lying at apropagation angle relative to said reference beam path so that saidsignal and reference beams intersect at a beam intersection lying withinsaid medium, said beam intersection having a size corresponding to beamareas of said reference and signal beams; producing a succession ofrelative displacements a direction parallel to said first axis betweensaid recording medium and said beam intersection of said signal andreference beam paths in synchronism with said succession of signalbeams, each of said displacements being less than said size of saidintersection whereby to record successive holograms partially overlappedalong a direction of said displacements; and further comprisingtemporarily halting said succession of signal beams after apredetermined number of said relative displacements have been producedand moving said recording medium and said beam intersection relative toone another until said beam intersection does not intersect the firstone of said holograms recorded with said succession of relativedisplacements, and then resuming the producing of a succession of signalbeams and the producing of a succession of relative displacements. 4.The method of claim 3 wherein said predetermined number of relativedisplacements is equal to M.
 5. The method of claim 4 wherein:saidsignal beam and said M amount of waves of said reference beam have awavelength, said recording medium has a thickness and said separationangle of said fan of M waves is at least approximately equal to##EQU19## wherein λ is the wavelength, L is the thickness, and θ_(S) isthe propagation angle; each of said displacements is of a length atleast approximately equal to ##EQU20## wherein λ is the wavelength and θis the separation angle.
 6. A method of recording successive hologramsin a recording medium, comprising:providing at least a fan of M amountof waves along at least a first axis with a separation angle betweenadjacent waves and directing said fan of M waves as a reference beamalong a reference beam path onto said recording medium; successivelymodulating a wave with a succession of images to produce a succession ofsignal beams along a signal beam path lying at a propagation anglerelative to said reference beam path so that said signal and referencebeams intersect at a beam intersection lying within said medium, saidbeam intersection having a size corresponding to beam areas of saidreference and signal beams; producing a succession of relativedisplacements a direction parallel to said first axis between saidrecording medium and said beam intersection of said signal and referencebeam paths in synchronism with said succession of signal beams, each ofsaid displacements being less than said size of said intersectionwhereby to record successive holograms partially overlapped along adirection of said displacements; wherein said providing comprisesproviding a two-dimensional fan of waves, said fan of M waves beingcomprised within said two-dimensional fan of waves, said two dimensionalarray comprising M waves along said first axis and N waves along asecond axis, said M waves of said first axis being separated by saidseparation angle and said N waves of said second axis being separated byan other separation angle, said method further comprising producing another relative displacement between said recording media and said beamintersection in a direction parallel to said second axis, said otherrelative displacement being less than said size of said beamintersection; and wherein said signal beam and said M amount of waves ofsaid reference beam have a wavelength, said signal beam has a bandwidthand said second axis and said signal beam path are approximately normalto one another and said other separation angle is approximately equal to

    √λ/L,

wherein λ is the wavelength and L is the thickness.
 7. A method ofrecording successive holograms in a recording medium,comprising:providing at least a fan of M amount of waves along at leasta first axis with a separation angle between adjacent waves anddirecting said fan of M waves as a reference beam along a reference beampath onto said recording medium; successively modulating a wave with asuccession of images to produce a succession of signal beams along asignal beam path lying at a propagation angle relative to said referencebeam path so that said signal and reference beams intersect at a beamintersection lying within said medium, said beam intersection having asize corresponding to beam areas of said reference and signal beams;producing a succession of relative displacements a direction parallel tosaid first axis between said recording medium and said beam intersectionof said signal and reference beam paths in synchronism with saidsuccession of signal beams, each of said displacements being less thansaid size of said intersection whereby to record successive hologramspartially overlapped along a direction of said displacements; whereinsaid providing comprises providing a two-dimensional fan of waves, saidfan of M waves being comprised within said two-dimensional fan of waves,said two dimensional array comprising M waves along said first axis andN waves along a second axis, said M waves of said first axis beingseparated by said separation angle and said N waves of said second axisbeing separated by an other separation angle, said method furthercomprising producing an other relative displacement between saidrecording media and said beam intersection in a direction parallel tosaid second axis, said other relative displacement being less than saidsize of said beam intersection; and wherein said signal beam and said Mamount of waves of said reference beam have a wavelength and said otherrelative displacement is approximately equal to ##EQU21## wherein λ isthe wavelength and θ' is the other separation angle of the second axis.8. A method of reconstructing at a detection plane successive hologramspreviously recorded in a recording medium by interfering a succession ofsignal beams with a reference beam including a fan of M amount of waves,said fan being parallel to the path of said signal beams and having aseparation angle between adjacent waves of the fan, while successivelydisplacing said medium relative to said signal and reference beams in adirection parallel to said first axis by a distance less than theintersection of said reference and signal beams in said recording mediumin synchronism with said succession of signal beams, said method ofreconstructing comprising:providing at least a fan of M amount of wavesalong at least a first axis corresponding to the direction of thereference beam with which said holograms were previously recorded with aseparation angle between adjacent waves and directing said fan of Mwaves as a reference beam along a reference beam path onto saidrecording medium; producing a succession of relative displacements adirection parallel to said first axis between said recording medium andsaid beam intersection of said signal and reference beam paths insynchronism with said succession of signal beams, each of saiddisplacements being equal to the distance of said displacements withwhich said holograms were previously recorded; detecting at saiddetection plane light diffracted from said reference beam by asuccession of said previously recorded holograms; and wherein said firstaxis and said signal beam path are parallel and said signal beam andsaid M amount of waves of said reference beam have a wavelength, saidrecording medium has a thickness and said separation angle of said fanof M waves is at least approximately equal to ##EQU22## wherein λ is thewavelength, L is the thickness, and θ_(S) is the propagation angle.
 9. Amethod of reconstructing at a detection plane successive hologramspreviously recorded in a recording medium by interfering a succession ofsignal beams with a reference beam including a fan of M amount of waves,said fan being parallel to the path of said signal beams and having aseparation angle between adjacent waves of the fan, while successivelydisplacing said medium relative to said signal and reference beams in adirection parallel to said first axis by a distance less than theintersection of said reference and signal beams in said recording mediumin synchronism with said succession of signal beams, said method ofreconstructing comprising:providing at least a fan of M amount of wavesalong at least a first axis corresponding to the direction of thereference beam with which said holograms were previously recorded with aseparation angle between adjacent waves and directing said fan of Mwaves as a reference beam along a reference beam path onto saidrecording medium; producing a succession of relative displacements adirection parallel to said first axis between said recording medium andsaid beam intersection of said signal and reference beam paths insynchronism with said succession of signal beams, each of saiddisplacements being equal to the distance of said displacements withwhich said holograms were previously recorded; detecting at saiddetection plane light diffracted from said reference beam by asuccession of said previously recorded holograms; and wherein saidsignal beam and said M amount of waves of said reference beam have awavelength and each of said relative displacements is of a length atleast approximately equal to ##EQU23## wherein λ is the wavelength and θis the separation angle.
 10. A method of reconstructing at a detectionplane successive holograms previously recorded in a recording medium bydiffracting a succession of signal beams with a reference beam includinga fan of M amount of waves, said fan being parallel to the path of saidsignal beams and having a separation angle between adjacent waves of thefan, while successively displacing said medium relative to said signaland reference beams in a direction parallel to said first axis by adistance less than the intersection of said reference and signal beamsin said recording medium in synchronism with said succession of signalbeams, said method of reconstructing comprising:providing at least a fanof M amount of waves along at least a first axis corresponding to thedirection of the reference beam with which said holograms werepreviously recorded with a separation angle between adjacent waves anddirecting said fan of M waves as a reference beam along a reference beampath onto said recording medium; producing a succession of relativedisplacements a direction parallel to said first axis between saidrecording medium and said beam intersection of said signal and referencebeam paths in synchronism with said succession of signal beams, each ofsaid displacements being equal to the distance of said displacementswith which said holograms were previously recorded; detecting at saiddetection plane light diffracted from said reference beam by asuccession of said previously recorded holograms; and further comprisingtemporarily halting said succession of signal beams after apredetermined number of said relative displacements have been producedand moving said recording medium and said beam intersection relative toone another until said beam intersection does not intersect the firstone of said holograms recorded with said succession of relativedisplacements, and then resuming the producing of a succession of signalbeams and the producing of a succession of relative displacements. 11.The method of claim 11 wherein said predetermined number of relativedisplacements is equal to M.
 12. The method of claim 11 wherein: saidsignal beam and said M amount of waves of said reference beam have awavelength, said recording medium has a thickness and said separationangle of said fan of M waves is at least approximately equal to##EQU24## wherein λ is the wavelength, L is the thickness, and θ_(S) isthe propagation angle;each of said displacements is of a length at leastapproximately equal to ##EQU25## wherein λ is the wavelength and θ isthe separation angle.
 13. A method of reconstructing at a detectionplane successive holograms previously recorded in a recording medium bydiffracting a succession of signal beams with a reference beam includinga fan of M amount of waves, said fan being parallel to the path of saidsignal beams and having a separation angle between adjacent waves of thefan, while successively displacing said medium relative to said signaland reference beams in a direction parallel to said first axis by adistance less than the intersection of said reference and signal beamsin said recording medium in synchronism with said succession of signalbeams, said method of reconstructing comprising:providing at least a fanof M amount of waves along at least a first axis corresponding to thedirection of the reference beam with which said holograms werepreviously recorded with a separation angle between adjacent waves anddirecting said fan of M waves as a reference beam along a reference beampath onto said recording medium; producing a succession of relativedisplacements a direction parallel to said first axis between saidrecording medium and said beam intersection of said signal and referencebeam paths in synchronism with said succession of signal beams, each ofsaid displacements being equal to the distance of said displacementswith which said holograms were previously recorded; detecting at saiddetection plane light diffracted from said reference beam by asuccession of said previously recorded holograms; wherein said providingcomprises providing a two-dimensional fan of waves, said fan of M wavesbeing comprised within said two-dimensional fan of waves, said twodimensional array comprising M waves along said first axis and N wavesalong a second axis, said M waves of said first axis being separated bysaid separation angle and said N waves of said second axis beingseparated by an other separation angle, said method further comprisingproducing an other relative displacement between said recording mediaand said beam intersection in a direction parallel to said second axis,said other relative displacement being less than said size of said beamintersection; and wherein said signal beam and said M amount of waves ofsaid reference beam have a wavelength, said signal beam has a bandwidthand said second axis and said signal beam path are approximately normalto one another and said other separation angle is approximately equal to

    √λ/L,

wherein λ is the wavelength and L is the thickness.
 14. A method ofreconstructing at a detection plane successive holograms previouslyrecorded in a recording medium by diffracting a succession of signalbeams with a reference beam including a fan of M amount of waves, saidfan being parallel to the path of said signal beams and having aseparation angle between adjacent waves of the fan, while successivelydisplacing said medium relative to said signal and reference beams in adirection parallel to said first axis by a distance less than theintersection of said reference and signal beams in said recording mediumin synchronism with said succession of signal beams, said method ofreconstructing comprising:providing at least a fan of M amount of wavesalong at least a first axis corresponding to the direction of thereference beam with which said holograms were previously recorded with aseparation angle between adjacent waves and directing said fan of Mwaves as a reference beam along a reference beam path onto saidrecording medium; producing a succession of relative displacements adirection parallel to said first axis between said recording medium andsaid beam intersection of said signal and reference beam paths insynchronism with said succession of signal beams, each of saiddisplacements being equal to the distance of said displacements withwhich said holograms were previously recorded; detecting at saiddetection plane light diffracted from said reference beam by asuccession of said previously recorded holograms; wherein said providingcomprises providing a two-dimensional fan of waves, said fan of M wavesbeing comprised within said two-dimensional fan of waves, said twodimensional array comprising M waves along said first axis and N wavesalong a second axis, said M waves of said first axis being separated bysaid separation angle and said N waves of said second axis beingseparated by an other separation angle, said method further comprisingproducing an other relative displacement between said recording mediaand said beam intersection in a direction parallel to said second axis,said other relative displacement being less than said size of said beamintersection; and wherein said signal beam and said M amount of waves ofsaid reference beam have a wavelength and said other relativedisplacement is approximately ##EQU26## wherein λ is the wavelength andθ' is the other separation angle of the second axis.